In this paper we are concerned with robust structure-preserving denoising filters for color images. We build on a recently proposed transformation from the RGB color space to the space of symmetric \(2\times 2\) matrices that has already been used to transfer morphological dilation and erosion concepts from matrix-valued data to color images. We investigate the applicability of this framework to the construction of color-valued median filters. Additionally, we introduce spatial adaptivity into our approach by morphological amoebas that offer excellent capabilities for structure-preserving filtering. Furthermore, we define color-valued amoeba M-smoothers as a generalization of the median-based concepts. Our experiments confirm that all these methods work well with color images. They demonstrate the potential of our approach to define color processing tools based on matrix field techniques.

Adaptive Filters for Color Images: Median Filtering and its Extensions

Today’s garbage classification is not fully automated and mostly relies on manual labor. In order to efficiently classify garbage and increase resource re-usability, society needs a modern solution. The development of artificial intelligence, especially in object detection, provides an excellent opportunity to develop real-time accurate garbage detection. This project is about real-time garbage detection using YOLOX and is used to detect seventeen categories of garbage. After the camera detects the garbage, it will automatically identify and analyze the type and specific the position of the garbage, which will be automatically picked up by a mechanical jaws. The datasets used in this paper consists of 5000 images with label. With the officially supported TensorRT optimization and acceleration technology, the model can be used in low-cost embedded devices and can detect garbage in near real-time without the need for a stable Internet connection. Our evaluation and comparison of these models includes some key metrics such as mean accuracy (mAP), inference time per frame, floating point operations(FLOPs), and the number of parameters of the model. The test results show that YOLOX’s mAP0.5:0.95 can exceed 97% and the inference speed can exceed 32 fps. The performance far exceeds that of other YOLO series, with high accuracy and speed in complex environments, making it highly applicable to today’s garbage classification needs.

YOLOX on Embedded Device With CCTV & TensorRT for Intelligent Multicategories Garbage Identification and Classification

In this paper we consider the fundamental operations dilation and erosion of mathematical morphology. It is well known that many powerful image filtering operations can be constructed by their combinations. We propose a fast and novel algorithm based on the Fast Fourier Transform to compute grey-value morphological operations on an image. The novel method may deal with non-flat filters and incorporates no restrictions on shape and size of the filtering window, in contrast to many other fast methods in the field. Unlike fast Fourier techniques from previous works, the novel method gives exact results and is not an approximation. The key aspect which allows to achieve this is to explore here for the first time in this context the umbra formulation of images and filters. We show that the new method is in practice particularly suitable for filtering images with small tonal range or when employing large filter sizes.

An Exact Fast Fourier Method for Morphological Dilation and Erosion Using the Umbra Technique

In this paper we consider the fundamental operations dilation and erosion of mathematical morphology. It is well known that many powerful image filtering operations can be constructed by their combinations. We propose a fast and novel algorithm based on the Fast Fourier Transform to compute grey-value morphological operations on an image. The novel method may deal with non-flat filters and incorporates no restrictions on shape and size of the filtering window, in contrast to many other fast methods in the field. Unlike fast Fourier techniques from previous works, the novel method gives exact results and is not an approximation. The key aspect which allows to achieve this is to explore here for the first time in this context the umbra formulation of images and filters. We show that the new method is in practice particularly suitable for filtering images with small tonal range or when employing large filter sizes. 

Abstract The basic filters in mathematical morphology are dilation and erosion. They are defined by a structuring element that is usually shifted pixel-wise over an image, together with a comparison process that takes place within the corresponding mask. This comparison is made in the grey value case by means of maximum or minimum formation. Hence, there is easy access to max-plus algebra and, by means of an algebra change, also to the theory of linear algebra. We show that an approximation of the maximum function forms a commutative semifield (with respect to multiplication) and corresponds to the maximum again in the limit case. In this way, we demonstrate a novel access to the logarithmic connection between the Fourier transform and the slope transformation. In addition, we prove that the dilation by means of a fast Fourier transform depends only on the size of the structuring element used. Moreover, we derive a bound above which the Fourier approximation yields results that are exact in terms of grey value quantisation. 

/pdf/properties-of-morphological-dilation-in-max-plus-and-plus-1p0g6z6d.pdf

Properties of Morphological Dilation in Max-Plus and Plus-Prod Algebra in Connection with the Fourier Transformation

The basic filters in mathematical morphology are dilation and erosion. They are defined by a flat or non-flat structuring element that is usually shifted pixel-wise over an image and a comparison process that takes place within the corresponding mask. Existing fast algorithms that realise dilation and erosion for grey value images are often limited with respect to size or shape of the structuring element. Usually their algorithmic complexity depends on these aspects. Many fast methods only address flat morphology.

Fast Morphological Dilation and Erosion for Grey Scale Images Using the Fourier Transform.

Sampling is a basic operation in image processing. In previous literature, a morphological sampling theorem has been established showing how sampling interacts with image reconstruction by morphological operations. However, while many aspects of morphological sampling have been investigated for binary images in classic works, only some of them have been extended to grey scale imagery. Especially, previous attempts to study the relation between sampling and grey scale morphology are restricted by construction to flat morphological filters. In order to establish a sampling theory for non-flat morphology, we establish an alternative definition for grey scale opening and closing relying on the umbra notion. Making use of this, we prove a sampling theorem about the interaction of sampling with fundamental morphological operations for non-flat morphology. This allows to make precise corresponding relations between sampling and image reconstruction, extending classic results for flat morphology of grey value images.

Sampling of Non-flat Morphology for Grey Value Images

The fundamental operations of mathematical morphology are dilation and erosion. In previous works, these operations have been generalised in a discrete setting to work with fields of symmetric matrices, and also corresponding methods based on partial differential equations have been constructed. However, the existing methods for dilation and erosion in the matrix-valued setting are not overall satisfying. By construction they may violate a discrete extremum principle, which means that results may leave the convex hull of the matrices that participate in the computation. This may not be desirable from the theoretical point of view, as the corresponding property is fundamental for discrete and continuous-scale formulations of dilation and erosion in the scalar setting. Moreover, if such a principle could be established in the matrix-valued framework, this would help to make computed solutions more interpretable.

Matrix Morphology with Extremum Principle

Sampling is a basic operation in image processing. In classic literature, a morphological sampling theorem has been established, which shows how sampling interacts by morphological operations with image reconstruction. Many aspects of morphological sampling have been investigated for binary images, but only some of them have been explored for grey-value imagery. With this paper, we make a step towards completion of this open matter. By relying on the umbra notion, we show how to transfer classic theorems in binary morphology about the interaction of sampling with the fundamental morphological operations dilation, erosion, opening and closing, to the grey-value setting. In doing this we also extend the theory relating the morphological operations and corresponding reconstructions to use of non-flat structuring elements. We illustrate the theoretical developments at hand of examples.

Vivek Sridhar

Papers

Fast Morphological Dilation and Erosion for Grey Scale Images Using the Fourier Transform.

Sampling of Non-flat Morphology for Grey Value Images

Matrix Morphology with Extremum Principle

An Exact Fast Fourier Method for Morphological Dilation and Erosion Using the Umbra Technique

Morphological Sampling Theorem and its Extension to Grey-value Images